Saturday, May 19, 2018
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Albert Einstein has done most of the work to build the general theory of relativity in the first place. David Hilbert competed and tried to scoop Einstein. Some folks have used the new classical theory to discuss black hole solutions – Schwarzschild, Kerr, Newman, and men like that. Others – Lemaitre, Friedmann, Robertson, Walker – have derived the big bang theory from that, and so on.

But a truly new era is associated with the name of Roger Penrose who began to play with some fancy modern aspects of Einstein's equations. Penrose brought the 1960s to general relativity. That decade means some new wind – but indeed, you may have mixed feelings about that new wind, indeed. Lots of people have good reasons to say that the human civilization peaked in that decade.

Penrose has always viewed Einstein's equations as a religion of a sort and his beliefs about the unknown aspects were always religiously shaped to some extent. One novelty of GR that everyone was aware of was the appearance of qualitatively new features of the – now dynamical – spacetime. Suddenly, horizons and singularities have emerged (as well as non-contractible loops and other novelties).

The singularity means an abrupt end to the spacetime – some place or moment (or the light-like compromise in between them) that makes it impossible to extend the spacetime to the future, to the past, or to the inside. The evolution is banned beyond that point if that singularity appears in the future; and the present is affected by unknown details about the initial singularity in the past.

Also, the charged or rotating black holes have two horizons, not just one. The exterior, event horizon defines the boundary of no return. When you cross it while you're falling into a black hole, it becomes even theoretically impossible to escape again. But the charged and rotating black holes also have the inner horizon. A strange aspect of this locus is that there are infinitely many ways to extend the spacetime geometry beyond that boundary – Einstein's equations cease to produce unique extensions.

Recall that Penrose viewed GR as a femme fatale and what we just discussed – especially singularities and inner horizons – seem somewhat pathological. They're the dirty laundry of Einstein's equations, even at the classical level. Penrose wanted to believe that GR always behaves as a true perfect lady so the dirty laundry had to be an illusion. Or there had to be another loophole, another excuse. So he invented the cosmic censorship hypotheses, the strong one and the weak one.

The weak one says that singularities that are formed in the spacetime from smooth initial data – like the singularities inside black holes – are never naked. It means that they can't affect measurements done at the future null infinity (where the future mankind will have enough space and apparatuses to measure most things very accurately). His intuition obviously was that all black holes and similar things that are born within Einstein's equations always cover their genitalia by underwear. So the weak cosmic censorship conjecture is that the evolution of generic initial data always creates the underwear to hide the sensitive organs from the future observer or, if you prefer a somewhat less intimate metaphor, a skirt protects the dirty laundry of a singularity.

Just to be sure, Penrose didn't hypothesize that he should be hired as the censor. He suggested that Nature itself – Einstein's equations, due to their imperfectly understood mathematical properties – automatically plays the role of the censor.

Analogously, the strong cosmic censorship conjecture (in geometers' heavy jargon, "global hyperbolicity") says that the inner horizons – which expose the situations in which Einstein's equations don't have a unique solution (instead, they have many) – are also avoided, for a different reason. These "Cauchy horizons" are claimed to be unstable. Whenever you add some generic perturbation involving matter obeying reasonable energy conditions, the perturbation grows exponentially and once you reach that horizon, the spacetime becomes singular. So in the real situation with perturbations, this other kind of dirty laundry – the unique-solution-busting inner horizon – is replaced with a singularity. That's also bad but not quite as bad because it censors the fact that in some situations, Einstein's equations have non-unique solutions.

He used the strong and weak "cosmic censorship conjecture" (CCC) terminology although the strong CCC should have been called more accurately as CFGM, the cosmic female genital mutilation, because that's what Penrose really proposed to do with these inconvenient inner organs of the black holes. Both conjectures may also be rephrased as saying that "the spacetime cannot be smoothly extended by Einstein's equations" in some situations. The assumptions about the situation where the extension is impossible are weaker in the case of the strong cosmic censorship, and that's why the strong cosmic censorship is stronger than the weak one.

OK, there has never been a terribly good reason to believe either of these hypotheses but both of them say that GR is kind of pretty or self-sufficient. GR doesn't have to be that pretty. It is clearly just an approximate theory. When the spacetime becomes singular or approaches the conditions of the inner horizons, new terms and new degrees of freedom may very well kick in and completely change the story – while keeping it consistent. But as a GR religious man, Penrose just wanted this external help to be unnecessary.

OK, as discussed in a very clear Quanta Magazine article by Kevin Hartnett,

dedicated to their teacher Demetrios Christodoulou (not to be confused with the 17-year-old Dimitrios Pagourtzis who was "born to kill" in Santa Fe, as his T-shirt on social networks said before he yelled "surprise" at the victims), mathematicians Dafermos (Princeton/Cambridge_UK) and Luk (Stanford) have shown that the inner horizon of the black holes are less unstable than Penrose thought.

So they proved that if you actually perturb the initial conditions a little bit, pretty much generically, it's still possible to extrapolate the spacetime (i.e. there still locally exists a solution of Einstein's equations) a finite piece beyond the inner horizon of the black hole. Penrose claimed that the very extrapolation of Einstein's equations drives the curvature to infinity and creates a singularity – and they just excluded the existence of this hypothetical singularity in the solutions with these generic, black-hole-like initial data.

Their spacetime may continue behind the "dirty laundry" where Penrose believed CFGM to be automatically applied. Well, Nature seems to demonstrably avoid CFGM at that point – after all, it's on par with climate skepticism, Justin Trudeau taught us. Nature abhors both censorship and female genital mutilation, Defermos and Luk demonstrated. However, on top of that, it seems to them that the spacetime may be continued into one that has to include an essential weak null singularity, a less brutal termination of the spacetime than Penrose's spacelike singularities.

These authors talk about a spacetime continued in a way that violates Einstein's equations. Unless I misunderstand something, I find it obvious that these comments are nothing else than guesswork. They're proposing that the laws of physics i.e. the rules of the game get changed in some way. Well, that's a problematic claim to talk about the modified rules of the game. And if you want to do so controllably, you should have a more general framework or theory that does not break down (e.g. the theory about effective field theories) which still tells you what is possible and what is not.

So these two authors have shown that the "end of the world" doesn't occur at the place or moment where Penrose predicted it, but they sort of propose a different "end of the world" that has to come later or further. Their new "end of the world" is null (i.e. light-like) and has different properties but I feel that their claims about this new locus are comparably shaky to Penrose's original claim.

Now, I haven't really read the full 217-page-long paper. But I've seen lots of pages of it and they looked impressive and persuasive enough. On top of that, Harvey Reall has had half a year to study these claims and still effectively agreed with the paper and praised it. Because I understand these matters much less than these professional general relativists, I have to partly build my beliefs on the conclusions by other people. I still feel uncomfortable that I have to do it – in much of physics, I really avoid it as much as I can – and my "sociological arguments" struggle to be closer to science than other people's mindless beliefs. So I actually know Harvey Reall, have listened to his talks, and have asked some questions to him. I have measured his ability to deal with Einstein's equations and judge the validity of claims similar to this new paper (e.g. those about the no-hair theorems – the lore that is really analogous to the cosmic censorship in many ways). He has passed my tests – he seems to know what he's talking about. And that's why I allow him to influence my opinions, too.

For years, you could have read several TRF blog posts that claimed that there's really no good reason to think that the cosmic censorship conjectures, as originally stated, are true. So this new paper allows me to say "I told you so". The violation of Penrose's beliefs is no inconsistency in mathematics. It just says that Einstein's equations allow you to extrapolate the spacetime further than previously thought, the spacetime behind that boundary isn't quite unique, so general relativity is more willing to show its dirty laundry than Penrose had suggested, and someone else – a more complete theory – has to guarantee that this dirty laundry doesn't lead to a full-blown societal collapse.

Singularities and inner horizons may be implied by GR and they may even be subjected to measurements, perhaps relatively accurate ones, in principle. GR may be unable to produce unique predictions for such measurements. But a more complete theory may produce unique measurements; and indeed, it may also happen that certain experiments may have fundamentally unpredictable outcomes.

Well, as long as the weak cosmic censorship conjecture is true in practice – the singularities can't "broadcast" their data to the future null infinity – we may still remain indifferent to the perceptions of the infalling observer. He may feel something inside the black hole, perhaps even some non-uniqueness of his measurements or perceptions, but it doesn't matter too much to the world and reproducible science because he's doomed.

Dafermos and Luk have done a lot of work which seems rigorous and impressive. But I think that they should abandon the Penrose-like guesswork-and-wishful-thinking approach to these matters. While they have settled a question – in a way that Penrose should find surprising – they have found some new questions that can't be fully answered right now. In such situations, people should honestly list all the possible big-picture answers they may think of. Saying "everyone should believe that this and that singularity should do this and that because it was our first guess and we're the most famous experts now" is simply not good enough science even though this is how Roger Penrose did it half a century ago.

Penrose has taught us that religious proselytization is less reliable than scientific evidence even if the religious proselytizer is celebrated as a top scientist.

I must say that you shouldn't think that I believe that Penrose was "completely" wrong about all these hypotheses. I also understand why "something like his conjectures" would be rather pretty and why it would form a coherent picture. But these conjectures were never reliable and the details could have been different. Some spirit of his conjectures may survive, however, or they may survive in a weakened form. For example, our Weak Gravity Conjecture has been shown basically equivalent to the weak CCC in some special context. The Weak Gravity Conjecture has some analogous shaky aspects as the CCC as well – unlike Penrose, I am warning you about those – but if these two seemingly different principles end up being so positively correlated, it is an extra reason to believe in both, perhaps in some clever generalized or weakened version of both.